Aims. We investigate whether the high energy tail detected by the
Fermi/LAT for the short GRB 081024B can be caused
by synchrotron and self-Compton emission in the context of either the internal or external
shock models.

Methods. For the internal shock scenario, we explore the possibility of
generating the high energy photons directly by means of the synchrotron process, or
inverse Compton emission in which target photons are synchrotron photons produced in
internal shocks taking place in a lately emitted shell (delayed internal shocks). In the
external shock scenario, we test whether the high energy tail can be an extension of the
afterglow synchrotron emission, or alternatively the inverse Compton component associated
with the afterglow synchrotron photons.

Results. For the internal shock scenario, we conclude that only an
inverse Compton component from delayed internal shocks can explain the high energy tail
that extends to the GeV range. In the external shock scenario, we show that the high
energy tail may be interpreted as synchrotron afterglow emission, if the slow cooling
phase starts as early as a few seconds after the trigger. On the other hand, the observed
high energy tail is consistent with an inverse Compton component of the afterglow in the
fast cooling regime.

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